A+ CATEGORY SCIENTIFIC UNIT

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## Mathematical Sciences Classification System

### 41Axx - Approximations and expansions {For all approximation theory in the complex domain, see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numerical approximation, see 65Dxx}

• 41A05
• 41A10
Approximation by polynomials {For approximation by trigonometric polynomials, see 42A10}
• 41A15
Spline approximation
• 41A17
Inequalities in approximation (Bernstein, Jackson, Nikol'skiĭ-type inequalities)
• 41A20
Approximation by rational functions
• 41A21
• 41A25
Rate of convergence, degree of approximation
• 41A27
Inverse theorems
• 41A28
Simultaneous approximation
• 41A29
Approximation with constraints
• 41A30
Approximation by other special function classes
• 41A35
Approximation by operators (in particular, by integral operators)
• 41A36
Approximation by positive operators
• 41A40
Saturation
• 41A44
Best constants
• 41A45
Approximation by arbitrary linear expressions
• 41A46
Approximation by arbitrary nonlinear expressions; widths and entropy
• 41A50
Best approximation, Chebyshev systems
• 41A52
Uniqueness of best approximation
• 41A55
• 41A58
Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)
• 41A60
Asymptotic approximations, asymptotic expansions (steepest descent, etc.) [See also 30E15]
• 41A63
Multidimensional problems (should also be assigned at least one other classification number in this section)
• 41A65
Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
• 41A80
Remainders in approximation formulas
• 41A99
None of the above, but in this section

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